The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups
Group Theory
2014-11-11 v2 Geometric Topology
Abstract
We use Klyachko's methods to prove that the natural map G to G-hat, where G is a torsion-free group and G-hat is obtained by adding a new generator t and a new relator w, is surjective only if w is conjugate to gt or gt^{-1} for some g in G. This solves a special case of the surjectivity problem for group extensions, raised by Cohen [Whitehead torsion, group extensions, and Zeeman's conjecture in high dimensions, Topology, 16 (1977) 79--88].
Keywords
Cite
@article{arxiv.math/0009101,
title = {The surjectivity problem for one-generator,, one-relator extensions of torsion-free groups},
author = {Marshall M Cohen and Colin Rourke},
journal= {arXiv preprint arXiv:math/0009101},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper5.abs.html